Problem: Solve for $x$ : $x^2 - 5x - 24 = 0$
Solution: The coefficient on the $x$ term is $-5$ and the constant term is $-24$ , so we need to find two numbers that add up to $-5$ and multiply to $-24$ The two numbers $-8$ and $3$ satisfy both conditions: $ {-8} + {3} = {-5} $ $ {-8} \times {3} = {-24} $ $(x {-8}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x + 3) = 0$ $x - 8 = 0$ or $x + 3 = 0$ Thus, $x = 8$ and $x = -3$ are the solutions.